Nested sampling [@Skilling2006] is a popular Monte Carlo method for computing Bayesian evidences and generating posterior samples given some likelihood and prior. Both standard nested sampling and its more general variant dynamic nested sampling [@Higson2017b] require sampling randomly from the prior within a hard likelihood constraint. This is a computationally challenging problem, and typically only be done approximately for practical problems. Popular methods include rejection sampling, utilized by MultiNest [@Feroz2008; @Feroz2009; @Feroz2013], and slice sampling, which is used by PolyChord [@Handley2015a; @Handley2015b] and dyPolyChord [@Higson2018dypolychord; @Higson2017b]. However all such approximate techniques can lead to additional errors, for example due to correlated samples or missing a mode of a multimodal posterior; for more details see [@Higson2018a].